
Our model has a Dirac fermion as DM and a real massive vector as mediator.
The model of Ref. [1]} postulates a real scalar or a vector field to be the dark force and a complex scalar or a fermion to be the dark matter.

The Stückelberg scalar model was introduced in order to maintain the gauge invariance in a QED-like theory with a massive real vector field. In this sense it provides an alternative to the Higgs mechanism. However, it needs an axionic scalar \(S\)  (\(\phi \)  in the notation of Ref. [2]}).

